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kumpel [21]
3 years ago
8

A ramp with a constant incline is made to connect a driveway to a front door. At a point 4 feet from the driveway, the height of

the ramp is 12 inches. At a point 6 feet from the driveway, the height of the ramp is 18 inches. What is the rate of change of the ramp's incline?
Mathematics
1 answer:
svetlana [45]3 years ago
3 0

Answer:

1/4 ft vertically per 1 ft horizontally, or 3inches per foot

Step-by-step explanation:

Translate these words into symbols:  One point is at (4 ft, 12 in) and the other is at (6 ft, 18 in).  Now find the slope of the line connecting these two points:

As we move from (4 ft, 12 in) to (6 ft, 18 in), x increases by 2 ft and y increases by (1/2) ft.

Thus, the slope of this line is m = rise / run = (1/2 ft) / (2 ft) = (1/4) ft per ft

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For this case, the first thing we must do is define variables.

We have then:

x: number of cabins

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We now write the equation that models the problem:

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We know that there are 148 campers.

Therefore, substituting y = 148 in the given equation we have:

148 = 28x

From here, we clear the value of x:

x = \frac{148}{28}\\x = 5.29

Therefore, the number of full cabins is:

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Answer:

The number of full cabins is:

x = 5

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